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We point out that after presenting our results on high $n$-$p$ momentum sensitivity of the $(d,p)$ cross sections in [Phys. Rev. Lett. 117 162502 (2016)] the last paragraph of our Letter refers to a need of going beyond the leading order of Weinberg state treatment. This task could be achieved by using any method that can provide exact solution of the three-body problem. Deltuva [arXiv:1806.00298] uses Faddeev equations to study the NN-model dependence of the $(d,p)$ cross sections. His results are consistent with a new study performed at Surrey which is undergoing a reviewing process at Physical Review C. Both studies discuss the $n$-$p$ sensitivity within three-body $n+p+A$ models with $NN$-independent $N$-$A$ optical potentials. The sensitivity may reappear in many-body treatment of $(d,p)$ reactions, for example, due to the threshold position dependence.
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The finite range adiabatic wave approximation provides a practical method to analyze (d,p) or (p,d) reactions, however until now the level of accuracy obtained in the description of the reaction dynamics has not been determined. In this work, we perform a systematic comparison between the finite range adiabatic wave approximation and the exact Faddeev method. We include studies of $^{11}$Be(p,d)$^{10}$Be(g.s.) at $E_p=$5, 10 and 35 MeV; $^{12}$C(d,p)$^{13}$C(g.s.) at $E_d=$7, 12 and 56 MeV and $^{48}$Ca(d,p)$^{49}$Ca(g.s.) at $E_d=$19, 56 and 100 MeV. Results show that the two methods agree within $approx 5%$ for a range of beam energies ($E_d approx 20-40$ MeV) but differences increase significantly for very low energies and for the highest energies. Our tests show that ADWA agrees best with Faddeev when the angular momentum transfer is small $Delta l=0$ and when the neutron-nucleus system is loosely bound.
Nucleon-knockout reactions on proton targets (p, pN ) have experienced a renewed interest due to the availability of inverse-kinematics experiment with exotic nuclei. Various theoretical descriptions have been used to describe these reactions, such as the Distorted-Wave Impulse Approximation (DWIA), the Faddeev-type formalism and the Transfer to the Continuum method. Our goal is to benchmark the observables computed with the Faddeev and Transfer to the Continuum formalisms in the intermediate energy regime relevant for the experimental (p, pn) and (p, 2p) studies. In this paper, we analyze the 11 Be(p,pn)10Be reaction for different beam energies, binding energies and orbital quantum numbers with both formalisms to assess their agreement for different observables. We obtain a good agreement in all cases considered, within 10%, when the input potentials are taken consistently and realistically.
The adiabatic distorted wave approximation (ADWA) is widely used by the nuclear community to analyse deuteron stripping ($d$,$p$) experiments. It provides a quick way to take into account an important property of the reaction mechanism: deuteron breakup. In this work we provide a numerical quantification of a perturbative correction to this theory, recently proposed in [R.C. Johnson, J. Phys. G: Nucl. Part. Phys. 41 (2014) 094005] for separable rank-one nucleon-proton potentials. The correction involves an additional, nonlocal, term in the effective deuteron-target ADWA potential in the entrance channel. We test the calculations with perturbative corrections against continuum-discretized coupled channel predictions which treat deuteron breakup exactly.
An improved description of single neutron stripping from $^{34,36,46}$Ar beams at 33 MeV/nucleon by a hydrogen target is presented and the dependence on the neutron-proton asymmetry of the spectroscopic factors is further investigated. A finite range adiabatic model is used in the analysis and compared to previous zero range and local energy approximations. Full three-body Faddeev calculations are performed to estimate the error in the reaction theory. In addition, errors from the optical potentials are also evaluated. From our new spectroscopic factors extracted from transfer, it is possible to corroborate the neutron-proton asymmetry dependence reported from knockout measurements.
Theoretical models of the (d,p) reaction are exploited for both nuclear astrophysics and spectroscopic studies in nuclear physics. Usually, these reaction models use local optical model potentials to describe the nucleon- and deuteron-target interactions. Within such a framework the importance of the deuteron D-state in low-energy reactions is normally associated with spin observables and tensor polarization effects - with very minimal influence on differential cross sections. In contrast, recent work that includes the inherent nonlocality of the nucleon optical model potentials in the Johnson-Tandy adiabatic-model description of the (d,p) transition amplitude, which accounts for deuteron break-up effects, shows sensitivity of the reaction to the large n-p relative momentum content of the deuteron wave function. The dominance of the deuteron D-state component at such high momenta leads to significant sensitivity of calculated (d,p) cross sections and deduced spectroscopic factors to the choice of deuteron wave function [Phys. Rev. Lett. {bf 117}, 162502 (2016)]. We present details of the Johnson-Tandy adiabatic model of the (d,p) transfer reaction generalized to include the deuteron D-state in the presence of nonlocal nucleon-target interactions. We present exact calculations in this model and compare these to approximate (leading-order) solutions. The latter, approximate solutions can be interpreted in terms of local optical potentials, but evaluated at a shifted value of the energy in the nucleon-target system. This energy shift is increased when including the D-state contribution. We also study the expected dependence of the D-state effects on the separation energy and orbital angular momentum of the transferred nucleon. Their influence on the spectroscopic information extracted from (d,p) reactions is quantified for a particular case of astrophysical significance.
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